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Table 1 Nomenclature of the variables and notation used in the paper

From: A multi-agent model to study epidemic spreading and vaccination strategies in an urban-like environment

Symbol Description
\(\mathcal {V}\) Set of all agents
\(\mathcal {L}\) Set of all locations
N Number of agents in the system
L Number of locations in the system
n Number of agents in each location
D Side of the square planar space
T Total number of discrete time-steps in the observation window
t Index for discrete time instants
Index for the locations in the system
i,j Indices for the agents in the system
ρ Density of location in the system
β(i) Function that maps agent i to its base location
Ω Region of space occupied by location
xi(t),yi(t) Position occupied by agent i in the planar space at time t
θi(t) Direction of the motion of agent i at time t
Φi(t) Angle of the direction of the shortest path from xi(t),yi(t) to Ωβ(i)
Δθit Angle drawn uniformly at random in [0,2π) for agent i at time t
v Velocity of agents outside their base location
α Randomness in the agents’ motion toward their base location
p Probability of jumping outside the base location
Pjump(d) Probability of jumping at a distance d from the base location
qin Probability of being inside the base location
qout Probability of being outside the base location
q Probability of being inside Ω
qout,d Probability of being at a distance d from the closest location
Ψin,Ψout,Ψd Probability that agents are inside, outside, and at a distance d
  from their base location
P(Σ) Probability density function of locations’ radii
γ Exponents of the power law distribution of locations’ radii
Σmin,Σmax Lower and higher cut-off of the distribution of locations’ radii
G(σ) Probability density function of agents’ radii of interaction
ω Exponents of the power law distribution of radii of interaction
σmin,σmax Lower and higher cut-off of the distribution of radii of interaction
ki Degree of agent i
λ Infection probability per contact
μ Recovery probability per unit time
s(t),i(t),r(t) Fraction of susceptible, infected, and recovered agents in the system
s(t),i(t),r(t) Fraction of susceptible, infected, and recovered agents in Ω
sout,d(t),iout,d(t),rout,d(t) Fraction of susceptible, infected, and recovered agents at distance d
  from the closest location
Λ(t) Contagion probability in Ω
Λout,d(t) Contagion probability at a distance d from the closest location
〈·〉 Statistical average of the quantity “ ·”
E [·] Expected value of the quantity “ ·”
P[·] Probability of an event “ ·”